Welcome to the forum.
You didn't address where you are located, how cold it was or whether you had any auxiliary heat or not... So, this is a "sort of guess"
Yes, you likely need a new regulator. Marshall regulators are probably some of the best. There are probably 2 regulators on your trailer. On the side with the "auto changeover regulator" is the one you were probably "fiddling with"... On the other side of the trailer you'll find a small "red high pressure regulator". Its purpose is to prevent liquid propane from flowing through the "crossover propane pipe". If I were you, I'd replace both regulators, however there may be nothing wrong with the regulators that you have, or it could be the "red high pressure regulator" that caused the lack of flow when the auto changeover regulator switch tanks. Some troubleshooting is in order...
You can download the 2012 Cougar brochure on the Keystone website. Here's the link:
https://www.keystonerv.com/media/239...-west-2012.pdf
There is, according to the brochure a 30K BTU furnace in the 2012 Cougar fifth wheels. Additionally, according to the brochure, the walls are R-9, the roof is R-14 and the floor, if you count the "foil bubble wrap" is R-29. When you consider the furnace efficiency is about 50-60% (30K BTU means only 15K to 18K BTU is actually heating the inside of your trailer. The rest is going out that little 2" hole and "heating the big outdoors"... Go out and put your hand near the furnace exhaust, you'll see what I mean.....
So, with 15-18 thousand BTU's in a poorly insulated "big box" with lots of single pane (R-1) windows, if it was "pushing 25F or so, you may not get a "comfortable trailer in an hour or less"... However, by morning, it should have been warm enough to at least walk to the bathroom in shirt sleeves.... So, you may have an issue with the regulator not delivering enough propane, but typically the furnace won't operate if it doesn't get the correct gas pressure and sense the appropriate flame.
Most people who camp in colder weather will augment the furnace with electric space heaters in the cabin. Realize that there's no heat under the floor from those electric heaters, so you will also need to run the furnace to protect the water lines and the holding tanks.
I hope this gets you started with answers to your questions. There's a wealth of information on the forum and a number of recent threads have addressed the propane system, the furnace and winter camping expectations... You should find enough reading to keep you busy for several days on the forum.
Again, welcome to the group.